RD Sharma Solutions Class 10 Mathematics Solutions for Some Applications Of Trigonometry Exercise 12.1 in Chapter 12 - Some Applications Of Trigonometry
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An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45° with the horizontal through the foot of the pole, find the length of the wire.
Solution:
A common notion in trigonometry, specifically, is the angle of elevation, which has to do with height and distance. It is described as an angle formed by the horizontal plane and an oblique line between the observer's eye and a target above it.
Given,
Height of the electric pole = 10 m = AB
The angle made by steel wire with ground (horizontal) θ = 45°
Let length of wire = L = AC
So, from the figure formed we have ABC as a right triangle.
\begin{aligned} &\sin \theta=\frac{\text { opposite side }}{\text { hypotenuse }} \\ &\sin 45^{\circ}=\frac{A B}{A C} \\ &\frac{1}{\sqrt{2}}=\frac{10 \mathrm{~m}}{\mathrm{~L}} \\ &\mathrm{~L}=10 \sqrt{2} \mathrm{~m} \\ &\therefore \text { Length of the wire }(\mathrm{L})=10 \sqrt{2} \mathrm{~m} \end{aligned}
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